document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466930>Question 466930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If n and p are integers greater than 1 and if p is a factor of both n+3 and n+10, what is the value of p?\r<BR>\n" );
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document.write( "The answer is 7, but I do not understand how they got this answer.\r<BR>\n" );
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document.write( "Can you help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #320258 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=320258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p a factor of n + 3 ==> n + 3 = rp, for some positive integer r\r<BR>\n" );
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document.write( "p a factor of n + 10 ==> n + 10 = sp, for some positive integer s\r<BR>\n" );
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document.write( "(n + 10 > n+ 3 ==> s > r.)\r<BR>\n" );
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document.write( "Hence (n+10) - (n+3) = sp - rp = (s-r)p, or (s-r)p = 7.  (Note that s-r is a positive integer.)\r<BR>\n" );
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document.write( "Hence  p divides the prime number 7 (divisors are 1 and 7.)\r<BR>\n" );
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document.write( "This means p = 7, since p > 1.   </SPAN>\n" );
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